In Minkowski space, linearised higher-spin extensions
of the Cotton tensor were constructed in the bosonic
[1]} and fermionic [2]} cases.
An alternative derivation of the higher-spin Cotton tensors
was given in [3]}, [4]}, where the latter played an integral role in establishing a conformal geometry of higher-spin gauge fields. Supersymmetric extensions of the higher-spin Cotton tensors were derived in
[2]}, [6]} for \({\cal N}=1\) , in [7]} for \(\mathcal {N}=2\)  and in [8]} for \({\cal N}>2\)  Poincaré supersymmetry.
It was argued in [9]}, [10]} that
higher-spin Cotton tensors exist on any conformally flat background, although explicit expressions for them in terms of Lorentz covariant derivatives and conformal prepotentials are difficult to derive if the spacetime curvature is non-vanishing. It is pertinent here to elaborate on these points in some more detail.
